Whakaoti i te 0.4x+0.9/0.5-0.1x-0.5/0.2=0.03+0.02x/0.03

$$\frac { 0.4 x + 0.9 } { 0.5 } - \frac { 0.1 x - 0.5 } { 0.2 } = \frac { 0.03 + 0.02 x } { 0.03 }$$

Whakaoti mō x

$$x=9$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawehea ia wā o 0.4x+0.9 ki te 0.5, kia riro ko \frac{0.4x}{0.5}+\frac{0.9}{0.5}.

$$\frac{0.4x}{0.5}+\frac{0.9}{0.5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Whakawehea te 0.4x ki te 0.5, kia riro ko 0.8x.

$$0.8x+\frac{0.9}{0.5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Whakarohaina te \frac{0.9}{0.5} mā te whakarea i te taurunga me te tauraro ki te 10.

$$0.8x+\frac{9}{5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Whakawehea ia wā o 0.1x-0.5 ki te 0.2, kia riro ko \frac{0.1x}{0.2}+\frac{-0.5}{0.2}.

$$0.8x+\frac{9}{5}-\left(\frac{0.1x}{0.2}+\frac{-0.5}{0.2}\right)=\frac{0.03+0.02x}{0.03}$$

Whakawehea te 0.1x ki te 0.2, kia riro ko 0.5x.

$$0.8x+\frac{9}{5}-\left(0.5x+\frac{-0.5}{0.2}\right)=\frac{0.03+0.02x}{0.03}$$

Whakarohaina te \frac{-0.5}{0.2} mā te whakarea i te taurunga me te tauraro ki te 10.

$$0.8x+\frac{9}{5}-\left(0.5x+\frac{-5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

Ka taea te hautanga \frac{-5}{2} te tuhi anō ko -\frac{5}{2} mā te tango i te tohu tōraro.

$$0.8x+\frac{9}{5}-\left(0.5x-\frac{5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

Hei kimi i te tauaro o 0.5x-\frac{5}{2}, kimihia te tauaro o ia taurangi.

$$0.8x+\frac{9}{5}-0.5x-\left(-\frac{5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

Ko te tauaro o -\frac{5}{2} ko \frac{5}{2}.

$$0.8x+\frac{9}{5}-0.5x+\frac{5}{2}=\frac{0.03+0.02x}{0.03}$$

Pahekotia te 0.8x me -0.5x, ka 0.3x.

$$0.3x+\frac{9}{5}+\frac{5}{2}=\frac{0.03+0.02x}{0.03}$$

Ko te maha noa iti rawa atu o 5 me 2 ko 10. Me tahuri \frac{9}{5} me \frac{5}{2} ki te hautau me te tautūnga 10.

$$0.3x+\frac{18}{10}+\frac{25}{10}=\frac{0.03+0.02x}{0.03}$$

Tā te mea he rite te tauraro o \frac{18}{10} me \frac{25}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$0.3x+\frac{18+25}{10}=\frac{0.03+0.02x}{0.03}$$

Tāpirihia te 18 ki te 25, ka 43.

$$0.3x+\frac{43}{10}=\frac{0.03+0.02x}{0.03}$$

Whakawehea ia wā o 0.03+0.02x ki te 0.03, kia riro ko \frac{0.03}{0.03}+\frac{0.02x}{0.03}.

$$0.3x+\frac{43}{10}=\frac{0.03}{0.03}+\frac{0.02x}{0.03}$$

Whakawehea te 0.03 ki te 0.03, kia riro ko 1.

$$0.3x+\frac{43}{10}=1+\frac{0.02x}{0.03}$$

Whakawehea te 0.02x ki te 0.03, kia riro ko \frac{2}{3}x.

$$0.3x+\frac{43}{10}=1+\frac{2}{3}x$$

Tangohia te \frac{2}{3}x mai i ngā taha e rua.

$$0.3x+\frac{43}{10}-\frac{2}{3}x=1$$

Pahekotia te 0.3x me -\frac{2}{3}x, ka -\frac{11}{30}x.

$$-\frac{11}{30}x+\frac{43}{10}=1$$

Tangohia te \frac{43}{10} mai i ngā taha e rua.

$$-\frac{11}{30}x=1-\frac{43}{10}$$

Me tahuri te 1 ki te hautau \frac{10}{10}.

$$-\frac{11}{30}x=\frac{10}{10}-\frac{43}{10}$$

Tā te mea he rite te tauraro o \frac{10}{10} me \frac{43}{10}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{11}{30}x=\frac{10-43}{10}$$

Tangohia te 43 i te 10, ka -33.

$$-\frac{11}{30}x=-\frac{33}{10}$$

Whakawehea ngā taha e rua ki te -\frac{11}{30}.

$$x=\frac{-\frac{33}{10}}{-\frac{11}{30}}$$

Tuhia te \frac{-\frac{33}{10}}{-\frac{11}{30}} hei hautanga kotahi.

$$x=\frac{-33}{10\left(-\frac{11}{30}\right)}$$

Whakareatia te 10 ki te -\frac{11}{30}, ka -\frac{11}{3}.

$$x=\frac{-33}{-\frac{11}{3}}$$